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Moving Charges & Magnetism Class 12 Physics Chapter 4 One Shot | New NCERT CBSE | Full chapter

LearnoHub - Class 11, 12・162 minutes read

The video illustrates the fundamental relationship between moving charges and magnetism, highlighting that static charges create electric fields while moving charges produce magnetic fields, and it incorporates practical examples and mathematical formulas to elucidate these concepts. Roshni emphasizes the historical context provided by Oersted's experiment, the significance of using tools like a galvanometer for measuring current, and the application of magnetic principles in real-life scenarios, such as transformers and circuit designs.

Insights

  • The video explains that static charges create electric fields, while moving charges are responsible for generating magnetic fields, highlighting the fundamental distinction between electricity and magnetism.
  • Roshni emphasizes the significance of practical examples and numerical problems in understanding magnetism, particularly for Class 12 Physics students, to make the concepts relatable and applicable.
  • Everyday items like fridge magnets and sliding doors serve as common examples of magnetism, demonstrating its relevance and presence in daily life.
  • The historical misconception that electricity and magnetism are separate phenomena is addressed, with Hans Christian Oersted recognized for his experiment that revealed their interconnection.
  • A magnetic compass is introduced as a practical tool for visualizing magnetic fields, showing how it points to magnetic north and helping to illustrate the directionality of magnetic fields.
  • Oersted's experiment, which involved observing a compass needle's deflection when current passed through a wire, serves as a foundational demonstration of how electric current produces a magnetic field.
  • The concept of a magnetic field is defined as a vector field (denoted by 'B') produced by moving charges, and it follows the principle of superposition, allowing for the calculation of net magnetic fields from multiple sources.
  • The Lorentz force is introduced as the total force experienced by a moving charge in electric and magnetic fields, with its formula (F = q(v × B)) highlighting the relationship between charge, velocity, and magnetic field.
  • The angle between a charge's velocity and the magnetic field is crucial, as it influences the magnitude of the magnetic force, with specific scenarios where the force can be zero if the vectors are parallel or antiparallel.
  • The magnetic force acts only on moving charges, and a stationary charge experiences no magnetic force due to its zero velocity, underscoring the necessity of motion for magnetic interactions.
  • The right-hand rule is explained as a method to determine the direction of magnetic force, where the orientation of the fingers and thumb provides a clear visual guide for understanding the relationship between velocity, magnetic field, and force.
  • The text discusses the application of Ampere's Circuital Law and the Biot-Savart Law in calculating magnetic fields, illustrating the mathematical relationships that govern the behavior of magnetic fields in various configurations, such as straight wires and coils.

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Recent questions

  • What is a moving coil galvanometer?

    A moving coil galvanometer is a device used to measure electric current. It operates on the principle that a current-carrying coil placed in a magnetic field experiences torque, causing it to rotate and move a pointer. The design typically includes a coil with many turns that can freely rotate about an axis, allowing it to respond effectively to the torque generated by the magnetic field. A coil spring is included to return the pointer to its zero position when no current is present, ensuring accurate readings. The galvanometer's sensitivity is enhanced by incorporating a soft iron core, which strengthens the magnetic field. The deflection of the pointer is directly proportional to the current flowing through the galvanometer, making it a reliable tool for measuring current in circuits.

  • How does a galvanometer measure current?

    A galvanometer measures current by utilizing a needle or pointer that deflects in response to the flow of electric current. When current flows through the coil of the galvanometer, it generates a magnetic field that interacts with the external magnetic field, resulting in a torque that causes the coil to rotate. The angle of deflection of the pointer is directly proportional to the amount of current passing through the coil, allowing for a visual representation of the current's magnitude. The relationship between the angle of deflection and the current is expressed mathematically, enabling accurate readings. Additionally, the galvanometer can be used in circuits like the Wheatstone bridge to detect current flow, remaining in a neutral position when no current is detected.

  • What is the purpose of a shunt resistor in a galvanometer?

    A shunt resistor is used in a galvanometer to enable it to measure larger currents without damage. Standard galvanometers are designed to handle only microamperes, so when measuring higher currents, a shunt resistor is added in parallel with the galvanometer. This configuration allows most of the current to bypass the galvanometer while only a small fraction flows through it, preventing overload. The shunt resistor must be carefully selected to ensure that it allows the galvanometer to read a specific small current (e.g., 10 µA) while the total current in the circuit can be significantly higher (e.g., 10 A). This setup ensures accurate readings and protects the galvanometer from excessive current.

  • How can a galvanometer be used as a voltmeter?

    A galvanometer can be modified to function as a voltmeter by adding a large resistor in series with it. This configuration allows the galvanometer to measure higher voltages while limiting the current flowing through it to a safe operating range. The large resistor ensures that the majority of the voltage drop occurs across it, while only a small voltage drop is present across the galvanometer itself. The value of this large resistor is determined using Ohm's Law, ensuring that the voltage drop across the galvanometer remains within its measurable range. Calibration is also necessary to adjust the readings based on the known values of the large resistor and the current flowing through the circuit, allowing for accurate voltage measurements.

  • What is the magnetic moment of a current loop?

    The magnetic moment of a current loop is a measure of the strength and direction of the magnetic field produced by the loop when current flows through it. It is calculated using the formula \( m = n \cdot i \cdot A \), where \( n \) is the number of turns in the loop, \( i \) is the current flowing through it, and \( A \) is the area of the loop. The magnetic moment indicates how the loop will interact with external magnetic fields, influencing its behavior in magnetic environments. A higher magnetic moment results from either an increase in the number of turns or a higher current, enhancing the loop's ability to generate a magnetic field. This property is crucial in applications such as electric motors and galvanometers, where the interaction between the magnetic moment and external fields is utilized for mechanical motion or measurement.

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Summary

00:00

Magnetism and Moving Charges Explained

  • The video discusses the relationship between moving charges and magnetism, emphasizing that static charges produce electric fields, while moving charges generate magnetic fields.
  • Roshni introduces the topic of magnetism in Class 12 Physics, highlighting the importance of understanding these concepts through practical examples and numerical problems.
  • Everyday examples of magnets include fridge magnets, cupboard door magnets, and sliding doors in malls and metro trains, illustrating the prevalence of magnetism in daily life.
  • The historical misconception that electricity and magnetism are unrelated is corrected, with Hans Christian Oersted credited for demonstrating their connection through a simple experiment.
  • A magnetic compass, which resembles a clock with a needle that points to magnetic north, is introduced as a tool to visualize magnetic fields and their directions.
  • Oersted's experiment involved passing current through a wire and observing the deflection of a nearby magnetic compass, demonstrating that a current-carrying conductor creates a magnetic field around it.
  • The video explains that when the direction of current is reversed, the deflection of the compass needle also reverses, indicating the relationship between current direction and magnetic field orientation.
  • The concept of a magnetic field is defined as a vector field denoted by 'B', which is produced by moving charges and obeys the principle of superposition, allowing for the calculation of net magnetic fields from multiple sources.
  • The video introduces the Lorentz force, which describes the total force experienced by a moving charge in both electric and magnetic fields, mathematically expressed as F = q(v × B).
  • The importance of the angle between the velocity of the charge and the magnetic field is highlighted, as it affects the magnitude of the magnetic force, with specific cases where the force can be zero if the vectors are parallel.

16:19

Understanding Magnetic Forces and Conductors

  • When velocity and magnetic fields are antiparallel, the angle (theta) between them can be 180°, which results in a magnetic force of zero, indicating no magnetic interaction in that scenario.
  • A stationary charge or object results in zero velocity (v = 0), leading to no magnetic force acting on it, as magnetic forces only affect moving charges.
  • The magnetic force is a vector quantity, dependent on the charge (q), velocity (v), and magnetic field (B), expressed mathematically as F = q * v × B, where the direction of the force is determined using the right-hand rule.
  • To determine the direction of the magnetic force, extend the right hand with fingers pointing in the direction of velocity (v) and curl them towards the magnetic field (B); the thumb will then point in the direction of the magnetic force (F).
  • The SI unit of magnetic force is Newton (N), while the magnetic field (B) can be derived from the equation F = q * v × B, leading to the unit Tesla (T), where 1 Tesla = 1 N/(C·m/s).
  • The smaller unit of magnetic field is Gauss (G), where 1 Gauss = 10^-4 Tesla, indicating that Tesla is a larger unit for measuring magnetic fields.
  • The discussion shifts to current-carrying conductors, where the magnetic force on a conductor can be calculated similarly to that of a single moving charge, using the expression F = I × L × B, where I is the current, L is the length of the conductor, and B is the magnetic field.
  • The total number of charge carriers (electrons) in a conductor can be calculated using the formula n * A * L, where n is the charge density, A is the cross-sectional area, and L is the length of the conductor.
  • Drift velocity (v_d) of electrons in a conductor is defined as the average velocity of charge carriers, which can be expressed as v_d = J/(n * e), where J is the current density, n is the charge density, and e is the charge of an electron.
  • An example problem involves a straight wire of length 1.5 meters carrying a current of 2 amps suspended in a uniform horizontal magnetic field, illustrating the application of these principles in real-life scenarios.

32:54

Magnetic Forces and Charged Particle Motion

  • The text discusses the concept of a rod suspended in a magnetic field, explaining that when the rod is in mid-air, the net force acting on it is zero, indicating a balance of forces.
  • The force experienced by a current-carrying rod in an external magnetic field is calculated using the formula \( F = i \cdot l \cdot B \cdot \sin(\theta) \), where \( i \) is the current, \( l \) is the length of the rod, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the rod and the magnetic field.
  • When the rod is horizontal and suspended in a magnetic field, the angle \( \theta \) is 90 degrees, simplifying the force calculation to \( F = i \cdot l \cdot B \) since \( \sin(90^\circ) = 1 \).
  • For a rod weighing 200 grams (0.2 kg), the gravitational force is calculated as \( F_g = m \cdot g = 0.2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 1.96 \, \text{N} \).
  • The magnetic field strength \( B \) is determined to be 0.65 Tesla when the current \( i \) is 1.5 Amperes and the length \( l \) of the rod is used in the force equation.
  • The text transitions to discussing the motion of charged particles in a magnetic field, emphasizing that the motion is influenced by the magnetic force acting on the particle.
  • A charged particle moving in a uniform magnetic field experiences a magnetic force that causes it to follow a circular path if the velocity is perpendicular to the magnetic field.
  • If the charged particle moves parallel to the magnetic field, the angle \( \theta \) is 0 degrees, resulting in no magnetic force acting on the particle, allowing it to continue in a straight line.
  • The overall motion of a charged particle in a magnetic field can be a helical path, combining circular motion due to the magnetic force and linear motion along the direction of the magnetic field.
  • The radius of the circular path, frequency of rotation, time period, and pitch of the helical motion are derived mathematically, with the pitch defined as the distance moved along the magnetic field in one complete rotation, calculated using the time period and the velocity parallel to the magnetic field.

49:17

Understanding the Biot-Savart Law Explained

  • The Biot-Savart Law describes the relationship between electric current and the magnetic field it generates, stating that the magnetic field at a point depends on the current flowing through a conductor, the length of the conductor, and the distance from the point to the conductor.
  • The magnetic field (B) produced by a current-carrying conductor is directly proportional to the amount of current (I) flowing through it; thus, higher current results in a stronger magnetic field, while lower current results in a weaker magnetic field.
  • The magnetic field also depends on the length element (dL) of the conductor, meaning that the contribution to the magnetic field from a small segment of the conductor is proportional to the length of that segment.
  • The distance (r) from the point of interest to the current-carrying conductor affects the magnetic field inversely; as the distance increases, the magnetic field strength decreases proportionally to the square of the distance (1/r²).
  • The direction of the magnetic field is perpendicular to the plane formed by the length element (dL) and the position vector (r) from the conductor to the point where the magnetic field is being calculated.
  • Mathematically, the differential magnetic field (dB) can be expressed as dB ∝ (I * dL * sin(θ)) / r², where θ is the angle between the length element and the position vector.
  • The complete expression for the magnetic field derived from the Biot-Savart Law is B = (μ₀/4π) * (I * dL * sin(θ)) / r², where μ₀ (the permeability of free space) is approximately 4π × 10⁻⁷ T·m/A.
  • The law is analogous to Coulomb's Law in electrostatics, as both describe long-range forces that are inversely proportional to the square of the distance between the source and the point of interest.
  • The principle of superposition applies to both laws, allowing for the calculation of the total magnetic field from multiple current sources by vector addition of the individual magnetic fields produced by each source.
  • In specific cases, such as a finite straight conductor or an infinite straight conductor, the magnetic field can be calculated using the derived expressions, taking into account the angles formed with respect to the point of interest.

01:06:22

Understanding Magnetic Fields and Coil Dynamics

  • The discussion begins with the concept of angles and their maximum value, which is established as 90°, emphasizing the relationship between the length of a line and the angle it forms as it increases in length.
  • The values of angles Th1 and Th2 are introduced, with a specific case where Th1 equals π/2, leading to a calculation involving the variable 'b' which is derived as 0i / 4πr * sin(90°), simplifying to 0i / (2πr).
  • The importance of understanding the expressions and derivations related to magnetic fields is highlighted, suggesting that while detailed mathematics may not be crucial for exams, grasping the underlying logic is essential.
  • A circular loop with radius R is introduced, and the distance x from its center to a point P is defined, leading to the integration of small elements to determine the magnetic field using Biot-Savart Law, resulting in the expression B = (0i / (2 * (x^2 + R^2)^(3/2))).
  • The magnetic field at the center of a coil is calculated by setting x to 0, yielding the formula B = (n * i) / (2R), which is crucial for understanding magnetic fields in coils.
  • For a coil with multiple turns (n turns), the magnetic field is expressed as B = (n * i) / (2R), reinforcing the concept that the magnetic field increases with the number of turns.
  • The magnetic field for a partial circular coil is derived as B = (0i1 / (4πR)) * θ, where θ is the angle in radians, emphasizing the importance of the angle in determining the magnetic field.
  • The right-hand rule is introduced for determining the direction of the magnetic field, where the thumb indicates the direction of the magnetic field and the fingers show the direction of current flow.
  • A practical example is provided where the magnetic field at a point O due to various segments of a semi-circular coil is calculated, demonstrating how to apply the derived formulas and the right-hand rule to find the net magnetic field.
  • A problem involving a tightly wound coil with 100 turns and a radius of 10 cm is presented, setting the stage for further calculations related to magnetic fields in coils, emphasizing the significance of the number of turns and the radius in determining the magnetic field strength.

01:21:26

Calculating Magnetic Fields in Coils and Wires

  • The problem involves calculating the magnetic field at the center of a coil with a radius of 10 cm (0.1 m) and 100 turns, carrying a current of 1 ampere. The formula used is B = (μ₀ * n * I) / (2 * r), where μ₀ = 4π × 10⁻⁷ T·m/A, n is the number of turns, I is the current, and r is the radius.
  • The magnetic field (B) at the center of the coil is calculated using the formula B = (μ₀ * n * I) / (2 * r). Substituting the values, we have B = (4π × 10⁻⁷ T·m/A * 100 * 1 A) / (2 * 0.1 m), which simplifies to B = 6.28 × 10⁻⁴ T.
  • The relationship between electrostatics and magnetism is highlighted, noting that Gauss's Law in electrostatics has a corresponding version in magnetism, known as Ampere's Circuital Law, which can be used to calculate magnetic fields.
  • Ampere's Circuital Law states that the integral of the magnetic field (B) around a closed loop is proportional to the current (I) passing through that loop, expressed mathematically as ∮B·dl = μ₀I.
  • To apply Ampere's Circuital Law, one must identify an appropriate loop (Amperean loop) around the current-carrying conductor, ensuring that the magnetic field is tangential to the loop at every point.
  • For a straight current-carrying conductor, the magnetic field can be calculated using Ampere's Circuital Law by integrating B around a circular path centered on the wire, leading to the expression B = (μ₀I) / (2πr), where r is the distance from the wire.
  • The magnetic field inside a circular cross-section of a wire carrying a steady current is uniform and can be calculated for points both inside (r < a) and outside (r > a) the wire's radius (a).
  • For points outside the wire (r > a), the magnetic field is inversely proportional to the distance from the wire, expressed as B ∝ 1/r, while for points inside the wire (r < a), the magnetic field can be determined by the enclosed current and the uniform current distribution.
  • The current density (J) is uniform across the wire's cross-section, allowing the calculation of the enclosed current (I₁) for any inner loop (r < a) as I₁ = I * (r₁² / a²), where r₁ is the radius of the inner loop.
  • The final expression for the magnetic field inside the wire (for r < a) is derived as B = (μ₀I * r₁) / (2πa²), demonstrating how the magnetic field varies with the distance from the center of the wire.

01:39:17

Magnetic Fields and Solenoids Explained

  • The magnetic field (b) is directly proportional to the distance (r) until r equals a, after which b becomes inversely proportional to r, indicating a decrease in b as r increases beyond a certain point.
  • Ampere's Circuital Law can be applied in symmetrical situations, such as calculating the magnetic field in a circular loop, where the magnetic field at the center is given by the formula \( \frac{0i}{2r} \).
  • A solenoid is defined as a tightly packed helix of wire, where each turn is closely spaced, resembling a cylinder, and insulation is necessary to prevent wire collisions, typically achieved using enamel wire.
  • The magnetic field inside a long solenoid can be calculated using the formula \( B = \mu_0 n I \), where \( n \) is the number of turns per unit length and \( I \) is the current flowing through the solenoid.
  • For a solenoid with a length of 0.8 meters and 2000 total turns, the number of turns per unit length (n) is calculated as \( n = \frac{2000}{0.8} = 2500 \) turns/meter.
  • The magnetic field inside the solenoid can be determined using \( B = \mu_0 n I \), where \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \) and \( I = 8 \, \text{A} \), resulting in \( B = 2.51 \times 10^{-2} \, \text{T} \).
  • The right-hand rule is used to determine the direction of the magnetic field, where curling fingers in the direction of current flow indicates the magnetic field direction, with the thumb pointing in the direction of the field.
  • When two current-carrying conductors are placed near each other, they exert forces on each other due to the magnetic fields they produce, which can either attract or repel depending on the direction of the currents.
  • The force exerted on one conductor by another can be calculated using the formula \( F = k \frac{I_a I_b}{d} \), where \( k \) is a constant, \( I_a \) and \( I_b \) are the currents in the conductors, and \( d \) is the distance between them.
  • Understanding the interaction between current-carrying conductors and their magnetic fields is crucial for applications in electromagnetism, such as in transformers, where solenoids are used to create magnetic fields from electric currents.

01:59:15

Forces and Interactions of Current-Carrying Conductors

  • The text discusses the interaction between two current-carrying conductors, specifically focusing on the forces exerted on each other, denoted as \( F_{b \text{ due to } a} \) and \( F_{a \text{ due to } b} \), which are equal in magnitude but opposite in direction, illustrating Newton's Third Law of Motion.
  • The expression for the force on conductor \( b \) due to conductor \( a \) is given as \( F = \frac{i_1 i_2}{2 \pi d} \cdot l \), where \( i_1 \) and \( i_2 \) are the currents, \( d \) is the distance between the conductors, and \( l \) is the length of the conductor segment experiencing the force.
  • The direction of the magnetic field created by a current-carrying conductor can be determined using the right-hand rule, where the thumb points in the direction of the current and the curled fingers indicate the direction of the magnetic field.
  • When both conductors carry current in the same direction, they attract each other, while if the currents flow in opposite directions, they repel each other, demonstrating the principle that parallel currents attract and anti-parallel currents repel.
  • The definition of an ampere is established as the current that, when maintained in each of two very long parallel conductors placed 1 meter apart in a vacuum, produces a force of \( 2 \times 10^{-7} \) Newtons per meter of length between them.
  • The torque experienced by a rectangular loop carrying current in a magnetic field is discussed, where the loop will rotate due to the forces acting on its sides when placed in the magnetic field.
  • The forces on each side of the rectangular loop are calculated using the right-hand rule, where the direction of the current and the magnetic field are used to determine the direction of the force acting on each segment of the loop.
  • The text emphasizes the importance of understanding the direction of forces and magnetic fields in determining the behavior of current-carrying conductors in various configurations.
  • The concept of torque is introduced as a rotational force that causes the loop to turn when subjected to an external magnetic field, highlighting the relationship between current, magnetic fields, and mechanical motion.
  • The overall discussion integrates fundamental physics principles, including electromagnetic theory and Newton's laws, to explain the interactions between currents and magnetic fields in practical scenarios.

02:15:16

Forces and Torque in Magnetic Fields

  • The text discusses the interaction of forces on a mango and an arm, indicating that a force is acting upward on the mango while a downward force is acting on the arm, illustrating basic principles of physics related to force direction and interaction.
  • It introduces the concept of current flow and magnetic fields, explaining that when current flows in a magnetic field, the resulting force can be calculated using the formula \( F = I \times B \), where \( F \) is the force, \( I \) is the current, and \( B \) is the magnetic field strength.
  • The text emphasizes that if the angle between the current direction and the magnetic field is 0 degrees, the force becomes zero, indicating that the forces acting on certain components (like the arms) may not contribute to movement.
  • Torque is introduced as a result of two forces acting on a loop in a magnetic field, explaining that when forces are applied at different lines, they can cause rotation, which is defined as torque.
  • The mathematical expression for torque is presented, stating that torque (\( \tau \)) can be calculated as \( \tau = F \times d \), where \( F \) is the force and \( d \) is the distance from the pivot point.
  • The text describes a rectangular coil placed in a magnetic field, detailing how to calculate the forces acting on each arm of the coil, specifically noting that forces on certain arms (like A and C) will be equal and opposite, resulting in a net force of zero.
  • It explains the application of the right-hand rule to determine the direction of forces, where the thumb indicates the direction of the force and the fingers indicate the direction of the magnetic field.
  • The net torque is calculated by considering the forces on the arms of the coil, with the torque being non-zero even when the net force is zero, due to the arrangement of forces causing rotation.
  • The text generalizes the situation by introducing an angle (\( \theta \)) between the magnetic field and the loop, explaining how to calculate the forces and torque in this scenario, emphasizing that the torque can be expressed as \( \tau = I \times A \times B \times \sin(\theta) \).
  • Finally, it concludes that the torque acting on a current loop in a magnetic field can be expressed as \( \tau = m \times B \), where \( m \) is the magnetic moment, and discusses the implications of the angle between the magnetic moment and the magnetic field on the resulting torque.

02:31:14

Magnetic Moments and Fields in Current Loops

  • The magnetic moment (m) of a circular current loop is calculated using the formula m = n * i * A, where n is the number of turns, i is the current, and A is the area of the loop. This indicates that the magnetic moment increases with more turns or higher current.
  • To find the magnetic field (B) at a point P located at a distance x from the center of a circular current loop, the formula is B = (μ₀ * n * i) / (2 * (R² + x²)^(3/2)), where R is the radius of the loop and μ₀ is the permeability of free space.
  • When the distance x is much larger than the radius R (x >> R), the expression simplifies to B = (μ₀ * n * i) / (2 * x³), indicating that the magnetic field decreases with the cube of the distance from the loop.
  • The area (A) of a circular loop is calculated as A = π * R², which can be substituted into the magnetic moment formula to express m in terms of the radius.
  • The magnetic field at the center of a circular coil with n turns, radius R, and carrying current i is given by B = (μ₀ * n * i) / (2 * R). For a coil with 100 turns and a radius of 10 cm carrying 3.2 A, the magnetic field calculates to 2 * 10^-3 Tesla.
  • The magnetic moment of the same coil is calculated as m = n * i * A, where A = π * R². For the given values, the magnetic moment is 10 A·m².
  • For a square coil with a side length of 10 cm and 20 turns carrying 12 A, the torque (τ) in a magnetic field (B) is calculated using τ = m * B * sin(θ), where θ is the angle with the magnetic field. The area of the square coil is A = L² = (0.1 m)².
  • The torque for the square coil in a magnetic field of 0.80 T at an angle of 30° is calculated to be 0.96 N·m, using the magnetic moment derived from the current and area.
  • The force (F) on a section of wire in a magnetic field is calculated using F = (μ₀ / (2π)) * (i₁ * i₂ * L) / d, where L is the length of the wire section and d is the distance between the wires. For a 10 cm section, the force calculates to 20 * 10^-6 Newtons.
  • A Moving Coil Galvanometer (MCG) is a device used to measure current and voltage in circuits, functioning based on the principles of electromagnetism, where a coil rotates in a magnetic field to indicate the current flow.

02:47:11

Understanding the Moving Coil Galvanometer

  • A galvanometer is a device used to measure electric current, featuring a needle or pointer that deflects in response to current flow, indicating the amount of current passing through it.
  • The operation of a moving coil galvanometer is based on the principle that a current-carrying coil placed in a magnetic field experiences torque, causing it to rotate and move the pointer.
  • The design of the galvanometer includes a coil with a large number of turns that is free to rotate about an axis, allowing it to respond effectively to the torque generated by the magnetic field.
  • A coil spring is incorporated into the design to ensure that when the current stops, the pointer returns to its zero position, providing a stationary reading when no current is present.
  • A uniform radial magnetic field is essential for the galvanometer's operation, as it ensures that the angle of deflection remains constant regardless of the coil's position, allowing for accurate current measurement.
  • The inclusion of a soft iron core within the galvanometer enhances the strength of the magnetic field, as soft iron can be easily magnetized, improving the device's sensitivity and accuracy.
  • The torque experienced by the coil is mathematically expressed as \( \tau = m \cdot B \cdot \sin(\theta) \), where \( m \) is the magnetic moment, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the magnetic field and the coil.
  • The deflection of the pointer is directly proportional to the current flowing through the galvanometer, with the relationship expressed as \( \phi \propto I \), where \( \phi \) is the angle of deflection and \( I \) is the current.
  • The moving coil galvanometer can serve multiple functions, including acting as a detector for current flow in circuits, functioning as an ammeter to measure current, and operating as a voltmeter to measure voltage.
  • The galvanometer's effectiveness as a detector is illustrated through its use in a Wheatstone bridge circuit, where it indicates whether current is flowing by remaining in a neutral position when no current is detected.

03:03:02

Using a Galvanometer for Current and Voltage Measurements

  • A galvanometer detects current flow by deflecting a needle; if current flows in one direction, the needle deflects to one side, and if it flows in the opposite direction, it deflects to the other side, indicating the current's direction and magnitude in microamperes (µA), specifically up to 10 µA.
  • To use a galvanometer as an ammeter capable of measuring larger currents (up to 10 amperes), modifications are necessary since a standard galvanometer can only handle microamperes without damage.
  • The solution involves adding a shunt resistor in parallel with the galvanometer, allowing most of the current to bypass the galvanometer while only a small fraction (10 µA) passes through it, preventing damage and enabling accurate readings.
  • The shunt resistor must be selected so that it allows the galvanometer to read 10 µA while the total current in the circuit is 10 A; thus, the shunt resistor must carry 9.99999 A.
  • To calculate the value of the shunt resistor (Rs), the relationship between the currents through the galvanometer (Ig) and the shunt (Is) must be established, where Is = I - Ig, with I being the total current.
  • The equivalent resistance of the circuit can be calculated using the formula for parallel resistances: 1/R_total = 1/Rg + 1/Rs, where Rg is the resistance of the galvanometer.
  • The galvanometer can also be modified to function as a voltmeter by using a large resistor in series, which allows it to measure higher voltages while limiting the current through the galvanometer to its safe operating range.
  • The large resistor must be chosen to ensure that the voltage drop across the galvanometer remains within its measurable range, while the majority of the voltage drop occurs across the larger resistor.
  • The value of the large resistor can be determined using Ohm's Law (V = IR), ensuring that the voltage drop across the galvanometer is minimal compared to the total voltage being measured.
  • Calibration of the galvanometer as a voltmeter involves adjusting the readings based on the known values of the large resistor and the current flowing through the circuit, allowing accurate voltage measurements.

03:18:02

Calculating Resistance with a Galvanometer

  • To determine the unknown resistance in a circuit using a galvanometer, apply the formula for current (I = V/R), where V is the voltage drop across the galvanometer and R is its resistance. If the galvanometer can measure up to 10 volts but only registers 1 millivolt, the unknown resistance can be calculated by rearranging the formula to R = V/I, where I is the current flowing through the circuit. This process involves connecting a small resistor in parallel to the galvanometer to enable it to function as an ammeter, or a large resistor in series to allow it to act as a voltmeter.
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